lecture3

# lecture3 - 1.225J(ESD 205 Transportation Flow Systems...

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Lecture 3 Lecture 3 Modeling Road Traffic Flow on a Link Modeling Road Traffic Flow on a Link Prof. Prof. Ismail Ismail Chabini and Prof. Chabini and Prof. Amedeo Odoni Amedeo Odoni 1.225 J (ESD 205) Transportation Flow Systems J (ESD 205) Transportation Flow Systems 1.225, 11/01/02 Lecture 3, Page 2 Lecture 3 Outline Lecture 3 Outline ± Time-Space Diagrams and Traffic Flow Variables ± Introduction to Link Performance Models ± Macroscopic Models and Fundamental Diagram ± Volume-Delay Function ± (Microscopic Models: Car-following Models ± Relationship between Macroscopic Models and Car-following Models) ± Summary

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1.225, 11/01/02 Lecture 3, Page 3 Time Time -Space Diagram: Analysis at a Fixed Position Space Diagram: Analysis at a Fixed Position h 1 h 2 h 4 h 3 T time position 0 0 L x 1.225, 11/01/02 Lecture 3, Page 4 Flows and Headways Flows and Headways ± m(x) : number of vehicles that passed in front of an observer at position x during time interval [0,T]. (ex. m(x)=5 ) ± Flow rate: ± Headway h j (x): time separation between arrival time of vehicles i and i+1 ± Average headway: ± What is the relationship between q(x) and ? T x m x q ) ( ) ( = ) ( ) ( ) ( ) ( 1 x m x h x h x m j j = = ) ( x h
1.225, 11/01/02 Lecture 3, Page 5 Flow Rate vs. Average Headway Flow Rate vs. Average Headway ± If T is large, ± Then, This is intuitively correct. ± q(t) is also called volume in traffic flow system circles (i.e. 1.225) ± q(t) is also called frequency in scheduled systems circles (i.e. 1.224) = ) ( 1 ) ( x m j j x h T ) ( ) ( ) ( ) ( ) ( 1 ) ( 1 x h x m x h x m T x q x m j j = = = ) ( 1 ) ( x h x q 1.225, 11/01/02 Lecture 3, Page 6 Time Time -Space Diagram: Analysis at Fixed Time Space Diagram: Analysis at Fixed Time t s 1 s 2 L 0 time position t 0

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1.225, 11/01/02 Lecture 3, Page 7 Density and Average Spacing Density and Average Spacing ± n(t): number of vehicles in a road stretch of length L at time t ± Density: ± s i (t): spacing between vehicle i and vehicle i+1 ± ± ± L t n t k ) ( ) ( = = ) ( 1 ) ( t n i i t s L ) ( ) ( ) ( ) ( ) ( 1 ) ( 1 t s t n t s t n L t k t n i i = = = ) ( 1 ) ( t s t k (Is this intuitive?) 1.225, 11/01/02 Lecture 3, Page 8 Performance Models of Traffic on a Road Link Performance Models of Traffic on a Road Link ± Link: a representation of a highway stretch, road from one intersection to the next, etc. ± Example of measures of performance: • Travel time • Monetary or environmental cost • Safety ± Main measure of performance: travel time ± 3 types of models: • Macroscopic models: Fundamental diagram (valid in static (stationary) conditions only. Long roads and long time periods) • Microscopic models: Car-following models (no lane changes) • Volume-delay functions
1.225, 11/01/02 Lecture 3, Page 9 Macroscopic Flow Variables Macroscopic Flow Variables ± Three macroscopic flow variables of a link:

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## This note was uploaded on 12/06/2011 for the course ESD 1.225j taught by Professor Ismailchabini during the Fall '02 term at MIT.

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lecture3 - 1.225J(ESD 205 Transportation Flow Systems...

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